EduSahara™ Worksheet

Question 1

1.

Identify the property by which the two given triangles are similar

(i)

not similar
(ii)

SAS Similarity
(iii)

AAA Similarity
(iv)

SSS Similarity

Question 2

2.

If the ratio of the bases of two triangles is H : I and the ratio of the corresponding heights is J : K , the ratio of their areas in the same order is

(i)

HK : IJ
(ii)

JK : HI
(iii)

HJ : IK
(iv)

IJ : HK
(v)

HI : JK

Question 3

3.

In the given figure, F is a point on side DE of △CDE such that ∠ECD = ∠CFE = 102° , ∠FEC = 24°. Find ∠ECF

(i)

53°
(ii)

55°
(iii)

52°
(iv)

56°
(v)

54°

Question 4

4.

In the given figure, △DEF ∼ △NOP and EF = 12 cm , OP = 16.8 cm and

(i)

76.83 sq.cm
(ii)

72.83 sq.cm
(iii)

75.83 sq.cm
(iv)

73.83 sq.cm
(v)

74.83 sq.cm

Question 5

5.

In the given figure, QR ∥ HI , and median GJ bisects QR.

If GJ = 15.3 cm, GK = 8.5 cm and GR = 9.44 cm, GI =

(i)

16.00 cm
(ii)

15.00 cm
(iii)

18.00 cm
(iv)

19.00 cm
(v)

17.00 cm

Question 6

6.

Which of the following are true?

a)	A sector is a polygonal region.
b)	A circle is a polygonal region.
c)	A triangle is a polygonal region.
d)	A semi-circle is a polygonal region.
e)	A square is a polygonal region.

(i)

{a,c}
(ii)

{b,e}
(iii)

{c,e}
(iv)

{b,e,c}
(v)

{d,a,c}

Question 7

7.

In the given figure, NOPQ is a trapezium in which

QR
=
(

x

+

40

)
cm, find the value of x

(i)

(

52

,

52

)
(ii)

(

50

,

49

)
(iii)

(

51

,

51

)
(iv)

(

52

,

50

)
(v)

(

50

,

50

)

Question 8

8.

△ABC is a triangle with sides BC = 11 cm, CA = 15 cm and AB = 12 cm. △ABC is reduced to △A'B'C' such that the smallest side of △A'B'C' is 5.5 cm. Find the corresponding lengths of the reduced triangle △A'B'C'.

(i)

4.5 cm, 6.5 cm, 5 cm
(ii)

5.5 cm, 7.5 cm, 6 cm
(iii)

3.5 cm, 5.5 cm, 4 cm
(iv)

7.5 cm, 9.5 cm, 8 cm
(v)

6.5 cm, 8.5 cm, 7 cm

Question 9

9.

In the given figure, points E , F and G are the mid-points of sides CD, DB and BC of △BCD. Which of the following are true?

a)	△FED ∼ △BCD
b)	△BGF ∼ △BCD
c)	△EGF ∼ △BCD
d)	△GCE ∼ △BCD
e)	△EFG ∼ △BCD

(i)

{c,e,a}
(ii)

{c,b}
(iii)

{c,d}
(iv)

{c,a}
(v)

{a,b,d,e}

Question 10

10.

Identify the property by which the two given triangles are similar

(i)

not similar
(ii)

SSS Similarity
(iii)

AAA Similarity
(iv)

SAS Similarity

Question 11

11.

In the given figure, △KLM is a triangle in which KN is the internal bisector of ∠K and MO ∥ NK meeting LK produced at O . ∠MOK =

(i)

∠LNK
(ii)

∠NKL
(iii)

∠OKM
(iv)

∠NMK
(v)

∠KNM

Question 12

12.

Which of the following are necessary conditions for similarity of two polygons ?

a)	The corresponding angles are equal.
b)	The corresponding sides are proportional.
c)	The corresponding angles are proportional.
d)	The corresponding sides are equal.

(i)

{c,b,a}
(ii)

{d,b}
(iii)

{c,d,a}
(iv)

{c,a}
(v)

{a,b}

Question 13

13.

In the given figure, ∠HIK = 47.23°, find the value of x =

(i)

41.77°
(ii)

42.77°
(iii)

40.77°
(iv)

43.77°
(v)

44.77°

Question 14

14.

The dimensions of the model of a multi-storey building are 1.5 cm ✕ 2 cm ✕ 7 cm. If the model is drawn to a scale of 1 : 170, find the floor area of a room of the building whose area in the model is 169 sq.cm.

(i)

463.41 sq.m
(ii)

488.41 sq.m
(iii)

470.41 sq.m
(iv)

501.41 sq.m

Question 15

15.

Which of the following are true?

a)	Area of a convex polygonal region is equal to the sum of the areas of all triangles formed by joining the vertices of the polygon with an interior point.
b)	Area of the union of two polygonal region is the sum of the individual area.
c)	A polygonal region can be divided into a finite number of triangles in a unique way.
d)	Area of the union of two polygonal region is not equal to the sum of the individual area.

(i)

{a,d}
(ii)

{b,c,a}
(iii)

{b,d,a}
(iv)

{b,a}
(v)

{c,d}

Question 16

16.

A model of a ship is made to a scale of 1 : 110. If the volume of the model ship is 729 cu.m, calculate the volume of the ship.

(i)

964299000.00 cu.m
(ii)

992299000.00 cu.m
(iii)

977299000.00 cu.m
(iv)

957299000.00 cu.m
(v)

970299000.00 cu.m

Question 17

17.

In the given figure, the altitudes SH and IT of △GHI meet at R. △RHI ∼

(i)

△THR
(ii)

△SIR
(iii)

△SIH
(iv)

△THI
(v)

△RTS

Question 18

18.

A model of a ship is made to a scale of 1 : 80. If the length of the ship is 1040 m, calculate length of the model ship.

(i)

18.00 m
(ii)

16.00 m
(iii)

13.00 m
(iv)

8.00 m
(v)

10.00 m

Question 19

19.

In the given figure, ∠HEF = ∠GEH and EH ∥ IG and EF = 20 cm, FH = 8 cm and HG = 7 cm. Find EI

(i)

19.50 cm
(ii)

17.50 cm
(iii)

16.50 cm
(iv)

18.50 cm
(v)

15.50 cm

Question 20

20.

In the given figure, △BDC is right-angled at D, DE ⟂ BC.

a)

ab
=
pc

b)

a

2
+
b

2
=
c

2

c)

d)

e)

1

a

2
+
1

b

2
=
1

p

2

(i)

{a,b,e}
(ii)

{d,b}
(iii)

{c,d,e}
(iv)

{c,a}
(v)

{c,a,b}

Question 21

21.

A triangle having an area 41.99 sq.cm is reduced such that the area of its image is 16.14 sq.cm. Find the scale factor.

(i)

8.62
(ii)

7.62
(iii)

0.62
(iv)

2.62
(v)

1.62

Question 22

22.

In the given figure, the parallelogram EFGH and the triangle △IEF are on the same bases and between the same parallels.

The area of the
△IEF
is x sq.cm. The area of the parallelogram is

(i)
thrice

the area of the triangle
(ii)
3
2

the area of the triangle
(iii)
twice

the area of the triangle
(iv)
5
4

the area of the triangle
(v)
4
3

the area of the triangle

Question 23

23.

In the given figure, the area of the △FGH is x sq.cm. I,J,K are the mid-points of the sides GH , HF and FG respectively. The area of the △IJK is

(i)
1
4

of area of △FGH
(ii)
3
4

of area of △FGH
(iii)
2
3

of area of △FGH
(iv)
1
3

of area of △FGH
(v)
1
2

of area of △FGH

Question 24

24.

The measurements of a triangular field △ABC are BC = 7 cm, AB = 15 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 24000. Calculate the actual area of the plot in sq.km.

(i)

5.02 sq.km
(ii)

3.02 sq.km
(iii)

4.02 sq.km
(iv)

1.02 sq.km
(v)

2.02 sq.km

Question 25

25.

In the given figure, given ∠EBC = ∠DBE, p = 7.5 cm, q = 9.5 cm and CD = 17 cm, find ED =

(i)

7.50 cm
(ii)

11.50 cm
(iii)

10.50 cm
(iv)

9.50 cm
(v)

8.50 cm

Assignment Key